When The World Is Running Down

As with "Walking on the Moon" and "Driven to Tears," "When the World Is Running Down, You Make the Best of What's Still Around" is distinct to The Police. 

If the vocal was removed from "When the World Is Running Down, You Make the Best of What's Still Around," you would still recognize the band based on the instrumental.  If the instrumental was removed, you would still recognize the band based on the vocal.  For this reason and many others, The Police is an iconic staple in rock music history.

On a side note -

Sting on his own has a distinct sound unique to him and can be recognized with or without the vocal.  One example is his album, Brand New Day.  I personally find Sting's music to be more emotional in tone as opposed to the tone that defined the band.

And so The Police, then, is a staple in my album collection.